Delta-rational chord: Difference between revisions

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which can be plugged back into the error formula to obtain the error. (We multiply the 1:''r''1:''r''2:...:''r''''n'' chord by α in order to compare it to the target DR chord on the same isodifferential series.)

This error measure is called '''least-squares delta error'''{{idiosyncratic}} (LSD error). LSD error does not depend on whether the chord whose error is being measured is 1:''r''1:''r''2:...:''r''''n'' or the same chord linearly shifted to have root α.

This error measure is called '''least-squares delta error'''{{idiosyncratic}} (LSD error). LSD error does not depend on whether the chord whose error is being measured is 1:''r''1:''r''2:...:''r''''n'' or the same chord linearly shifted to have root α. Unfortunately, LSD error does not form a metric on the set of delta signatures with a fixed number of terms. There is ongoing research seeking a natural and psychoacoustically useful metric space structure on delta signatures.

Unfortunately, LSD error does not form a metric on the set of delta signatures with a fixed number of terms. There is ongoing research seeking a natural and psychoacoustically useful metric space structure on delta signatures.

==== Partially DR ====

@@ Line 73: / Line 73: @@
 which can be plugged back into the error formula to obtain the error. (We multiply the 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> chord by α in order to compare it to the target DR chord on the same isodifferential series.)
-This error measure is called '''least-squares delta error'''{{idiosyncratic}} (LSD error). LSD error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root α.
+This error measure is called '''least-squares delta error'''{{idiosyncratic}} (LSD error). LSD error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root α. Unfortunately, LSD error does not form a metric on the set of delta signatures with a fixed number of terms. There is ongoing research seeking a natural and psychoacoustically useful metric space structure on delta signatures.
-Unfortunately, LSD error does not form a metric on the set of delta signatures with a fixed number of terms. There is ongoing research seeking a natural and psychoacoustically useful metric space structure on delta signatures.
 ==== Partially DR ====